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Volume 54 Issue 5
May  2022
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Guo Ziyi, Zhao Jianfu, Li Kai, Hu Wenrui. Bifurcation analysis of thermocapillary convection based on POD-Galerkin reduced-order method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1186-1198 doi: 10.6052/0459-1879-21-642
Citation: Guo Ziyi, Zhao Jianfu, Li Kai, Hu Wenrui. Bifurcation analysis of thermocapillary convection based on POD-Galerkin reduced-order method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1186-1198 doi: 10.6052/0459-1879-21-642


doi: 10.6052/0459-1879-21-642
  • Received Date: 2021-12-03
  • Accepted Date: 2022-03-07
  • Available Online: 2022-03-08
  • Publish Date: 2022-05-01
  • Thermocapillary convection is driven by surface tension gradient caused by temperature gradient. The flow is subject to nonlinear interactions between convection and heat transfer, so it has complex transition behaviors. It is significant to investigate the flow bifurcation phenomenon as parameters in the governing equations change. The POD-Galerkin reduced-order method is a fast fluid computational method, based on proper orthogonal decomposition and Galerkin projection. The numerical bifurcation method finds the parameter values at which bifurcation exists by computing the asymptotic flow states and bifurcation points directly. In order to tackle flow transition problems in a more efficient way, a combination of direct numerical simulation, POD-Galerkin reduced-order method and numerical bifurcation method is applied to investigate the transition behavior of thermocapillary convection in a liquid layer. The POD reduced-order model of thermocapillary convection in a 2D cavity under different volume ratios is established and its bifurcation diagram is obtained by numerical bifurcation method. The validity of such a model for Reynolds numbers and volume ratios that are different from those for which the model is derived is studied and the possibility of modelling thermocapillary flow in a simple geometry over a range of flow parameters is assessed. Compared with the results obtained by direct numerical simulation, the accuracy and robustness of the low-order model are verified. The results show that the reduced-order model reflects qualitatively similar flow characteristics to the original high-order system, and quantitively, the relative error of frequency of periodic solution of the reduced-order model to that obtained by the direct numerical simulation is around 5%. Hence, the feasibility of the POD-Galerkin reduced-order method on thermocapillary convection is confirmed.


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